Question

If P represents radiation pressure, C represents speed of light and Q represents radiation energy striking a unit area per second, then non-zero integers x, y and z such that $P^{x}Q^{y}C^{z}$ is dimensionless, are

• A. $x = 1,y = 1,z = - 1$
• B. $x = 1,y = - 1,z = 1$
• C. $x = - 1,y = 1,z = 1$
• D. $x = 1,y = 1,z = 1$

Answer 1

Answer: (B)

$x = 1,y = - 1,z = 1$

Answer 2

$\lbrack P^{x}Q^{y}C^{z}\rbrack = M^{0}L^{0}T^{0}$

By substituting the dimension of each quantity in the given expression

$\lbrack ML^{- 1}T^{- 2}\rbrack^{x}\lbrack MT^{- 3}\rbrack^{y}\lbrack LT^{- 1}\rbrack^{z} = \lbrack M^{x + y}L^{- x + z}T^{- 2x - 3y - z}\rbrack = M^{0}L^{0}T^{0}$

by equating the power of M, L and T in both sides: $x + y = 0$, $- x + z = 0$ and $- 2x - 3y - z = 0$

by solving we get $x = 1,y = - 1,z = 1$.